ELA, Volume 9, pp. 282-289, October 2002, abstract.  

Non-trivial Solutions to Certain Matrix Equations

Aihua Li and Duane Randall

The existence of non-trivial solutions to matrix equations 
of a very general type over the real numbers is investigated 
in this paper. The Lefschetz Fixed Point Theorem guarantees 
the existence of special orthogonal matrix solutions to these 
equations whenever the given matrices in the defining equations 
belong to the special orthogonal group. A particular matrix 
equation is studied in detail. General conditions are elaborated 
under which no non-trivial solutions exist for this particular
matrix equation.